Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions

In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral fractional Sturm–Liouville problem and discuss the orthogona...

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Autores principales: Klimek, Malgorzata, Ciesielski, Mariusz, Blaszczyk, Tomasz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8871260/
https://www.ncbi.nlm.nih.gov/pubmed/35205439
http://dx.doi.org/10.3390/e24020143
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author Klimek, Malgorzata
Ciesielski, Mariusz
Blaszczyk, Tomasz
author_facet Klimek, Malgorzata
Ciesielski, Mariusz
Blaszczyk, Tomasz
author_sort Klimek, Malgorzata
collection PubMed
description In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral fractional Sturm–Liouville problem and discuss the orthogonality of eigenvectors. Finally, we present the numerical results for the considered problem obtained by utilizing the midpoint rectangular rule.
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spelling pubmed-88712602022-02-25 Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions Klimek, Malgorzata Ciesielski, Mariusz Blaszczyk, Tomasz Entropy (Basel) Article In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral fractional Sturm–Liouville problem and discuss the orthogonality of eigenvectors. Finally, we present the numerical results for the considered problem obtained by utilizing the midpoint rectangular rule. MDPI 2022-01-18 /pmc/articles/PMC8871260/ /pubmed/35205439 http://dx.doi.org/10.3390/e24020143 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Klimek, Malgorzata
Ciesielski, Mariusz
Blaszczyk, Tomasz
Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions
title Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions
title_full Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions
title_fullStr Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions
title_full_unstemmed Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions
title_short Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions
title_sort exact and numerical solution of the fractional sturm–liouville problem with neumann boundary conditions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8871260/
https://www.ncbi.nlm.nih.gov/pubmed/35205439
http://dx.doi.org/10.3390/e24020143
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AT ciesielskimariusz exactandnumericalsolutionofthefractionalsturmliouvilleproblemwithneumannboundaryconditions
AT blaszczyktomasz exactandnumericalsolutionofthefractionalsturmliouvilleproblemwithneumannboundaryconditions

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